Thread: magic circles?

Can anyone help me understand how to arrange the digits (odd only) 9-25 in a magic circle so that the sum of the numbers in each straight line is the same? There is one circle inthe middle and 8 around it. There must be a formula to this. Thank you.

Hello, gager23!

Arrange the odd numbers from 9 to 25 in a magic circle
so that the sum of the numbers in each straight line is the same.
There is one circle inthe middle and 8 around it.

There really isn't any formula for this, but there is a very logical procedure.



Isn't it reasonable to put the middle number in the center of the circle?


Next, take pairs of numbers "from each end": .
. . Note that the pairs have the same sum: 34.

Place the pairs on opposite ends of a diameter.


Then one possible solution looks like this:

Code:

              * 9 *
          *     |     *
       19       |       11
       *  \     |     /  *
            \   |   /
      *       \ | /       *
     21 - - - -17 - - - - 13
      *       / | \       *
            /   |   \
       *  /     |     \  *
       23       |       15
          *     |     *
              *25 *

Thanks for the reply--it makes sense and is appreciated.